1. Field of Invention
This invention relates to electronic means to provide a velocity signal for a piezoelectric positioner and the use of this velocity signal to provide damping of the mechanical vibrations thereof.
2. Description of Prior Art
Many positioning systems have a position response related to an applied control signal voltage. Piezoelectric materials have the capacity to convert electric potentials into mechanical strains and vice versa. Thus a piezoelectric positioner has an output position that is substantially linearly proportional to an applied control voltage. Examples of piezoelectric positioner use are the positioning of a micromirror in an optical switch by Riza et al in U.S. Pat. No. 5,208,880, the positioning of a catcher tube in a catcher tube particle sorter by North in U.S. Pat. No. 5,030,002, and the psitioning of a surface in an acoustical loudspeaker. Such positioners often have very little mechanical damping resulting in undesireable resonances or overshoots in position followed by poorly damped oscillations.
One means to dampen position oscillations or resonances is to use mechanical damping devices whereby a retarding force is produced by a position velocity. This mechanical damping can be provided by dashpots, by immersing the moving structure in a viscous fluid, or by other well known means. Such added mechanical damping often adds substantial mass to the positioner which reduces its speed of response and its resonant frequency as well as adding significant cost, size, and complexity to the positioner system.
Another method to dampen position oscillations is to produce a position velocity signal which can be negatively fed back into the driving circuitry to oppose the velocity and thereby reduce the oscillations. This velocity signal may be derived directly from a velocity sensor or indirectly by generating the time derivative of a position sensor signal. Ravizza in U.S. Pat. No. 4,080,636 teaches the use of a piezoelectric position sensor mounted adjacent a piezoelectric actuator to sense the actuator position. This method works very well but cannot be used in some positioner applications due to constraints on cost, size, and mass added to the positioner.
One approach to minimizing unwanted position overshoots and poorly damped oscillations is to shape the input driving waveform. This is taught by Singer et al in U.S. Pat. No. 4,916,635 entitled xe2x80x9cShaping Command Inputs To Minimize Unwanted Dynamicsxe2x80x9d and is further elaborated on in U.S. Pat. No. 5,638,267 by Singhouse et al. This approach works well when the system""s natural resonant frequency and damping are accurately known. However, this approach suffers from the following limitations:
The time to attain a reasonably stable change in position in response to a step input signal is much greater than that which can be attained by a system having about 70% of critical damping where the final position is reached in about 0.52 of the period of the system natural resonant frequency. With a shaped input signal the time to reach final position is greater than the period of the natural resonant frequency.
The system has no improvement in resistance to oscillations induced by external vibrations or by factors other than the input signal.
The system has no improvement in response when the driving signal must be sinusoidal as in the case of an acoustical loudspeaker.
The system response is sensitive to inaccuracies of knowledge of the system natural frequency and damping.
The system response is sensitive to changes in system natural frequency and darting due to changes in temperature, load, ageing, wear, and the like.
Another approach is to use a trapezoidal driving signal where the rise, dwell, and fall times are all equal to the period of the system natural resonance frequency. The utility of this approach is based on the fact that this waveform has no Fourier series components at the system natural resonance frequency. This method suffers from the limitations of the previous case.
An approach to providing electronic damping of a piezoelectric positioner is taught by Walker et al in U.S. Pat. No. 5,714,831. This approach does not sense the positioner velocity. Instead it constructs a model impedance having dynamic characteristics substantially identical to those of the positioner and driven by the same command voltage applied to the positioner. The velocity signal is then derived from the model impedance and used to modify the command voltage applied to the positioner and the model impedance. This approach requires that the model impedance accurately represent the positioner and may require a position sensor to correct the model for any inaccuracies. This approach also provides no improvement in resistance to mechanical oscillations induced by external vibrations or to factors other than the input command signal.
The problem of providing damping to a piezoelectric positioner can be understood by examining the Electrical Substitute Circuit Diagram shown on FIG. 1. This diagram is well known and is shown on U.S. Pat. No. 5,714,831, FIG. 14 and U.S. Pat. No. 5,675,296, FIG. 4. This diagram is derived from the complete equivalent circuit by omitting the di-electric loss resistance which is much greater than the impedance of the static capacitance C0 or the dynamic impedance portion of the piezoelectric positioner comprising L1R1C1 in series. C0 is the static capacitance of the positioner with no motion. L1 represents the combined load mass and the positioner distributed mass. C1 represents the compliance of the positioner and its support structure. R1 represents the system damping produced by positioner internal and external energy losses during motions. The positioner movement is directly proportional to the voltage across C1 and vice versa. Electrical energy is stored in C0 and mechanical energy is stored in C1 and L1. Positioner velocity is proportional to the current through C1 which is not directly available for measurement.
A typical piezoelectric positioner has an impedance magnitude and phase angle similar to that shown on FIG. 2. This positioner impedance has a zero at f0 where the inductive reactance of L1 is canceled by the capacitive reactance of C1 and the current through L1R1C1 is determined by R1. R1 is typically very small for poorly damped positioners. Thus, driving voltages at f0 produce large currents through C1 with correspondingly large positioner motions.
This positioner impedance has a pole at fp where the inductive reactance of L1 is canceled by the capacitive reactance of C0 and C1 in series and thus fp is greater than f0. At fp the impedance of L1R1C1 in series is greater than that at f0 and the current through C1 is much lower and the positioner motions are much smaller.
Even when a step change in driving voltage is applied to a positioner through a series resistor there are often poorly damped oscillations of positioner motion. This is shown on FIG. 3 for two values of resistance in series with a Polytec Optronics, Inc. P-173 linear positioner. The time required for a single oscillation is about 180 microseconds but it takes 700 to 1000 microseconds for the oscillations to decay substantially. More damping is clearly required.
The response of a series LRC circuit to a step input of voltage is shown on FIG. 4 for various values of zeta, the fraction of critical damping present. There is a large overshoot of capacitor finel voltage and poorly damped oscillations when the damping is 0.2 of critical damping. Piezoelectric positioners and their attached loads often have damping as low as 0.05 to 0.10 of critical damping. When the damping is about 0.7 of critical damping the final voltage is reached in xcfx890t=3.285 or t=0.5228/f0 seconds and the overshoot is about 0.05 of the voltage change. More damping, such as 0.8 of critical damping, reduces the overshoot to about 0.01 of the voltage change.
Accordingly, several objects and advantages of my invention are:
(a) to provide damping to a piezoelectric positioner by electronic means thereby permitting rapid position changes with little or no overshoot or oscillations of position.
(b) to provide electronic damping to a piezoelectric positioner without requiring the use of a velocity sensor or a position sensor.
(c) to provide electronic damping to a piezoelectric positioner which may be completely implemented by a few, simple, low cost components such as a capacitor, a few resistors, and a few operational amplifiers.
(d) to provide electronic damping to a piezoelectric positioner which is unaffected by changes in the natural frequency of oscillation of the positioner and its attached load.
(e) to provide electronic damping to a piezoelectric positioner the design of which requires no knowlwdge of the natural frequency of oscillation of the positioner and its load.
(f) to provide electronic damping of a piezoelectric positioner whereby the damping can be easily adjusted by resetting of one or two potentiometers in the electronic damping circuit.
(g) to provide electronic damping to a piezoelectric positioner and its load of up to critical damping or more and thereby provide greatly increased resistance to disturbances in position caused by external vibrations whereby the need for vibration isolation means and its associated cost may be reduced or eleiminated.
(h) to provide electronic damping to a piezoelectric positioner and its load of up to critical damping or more thereby removing restrictions on the shape of the driving waveform to obtain rapid position response without overshoots or poorly damped oscillations.
(i) to provide electronic damping to a piezoelectric positioner and thereby reduce or eliminate undesireable first order position resonances.
Further objects and advantages are to provide electronic damping to a piezoelectric positioner which can be easily designed and manufactured, which is esy to use, which is inexpensive, which is easily incorporated into new driving circuit designs and which is easily added to existing circuit hardware, which can tolerate changes in positioner dynamic characteristics without loss of damping performance, and which can significantly increase the ability of a piezoelectric positioner to move a load from one position to another rapidly and stably without objectionable overshoots and oscillations of position.
Still further objects and advantages will become apparent from a consideration of the ensuing description and drawings.